Random Variable

Many real-life decisions are made by assigning probabilities to all possible outcomes of a particular situation. For example, a bank's lender specializes in obtaining loan approvals for start-ups. The lender can compute the probability that they will get zero, one, two, etc loans a month.

Continuous random variables cannot be counted, but they can be measured. A continuous random variable has an uncountable number of possible outcomes, which is represented by an interval on the real number line.

• can take on an infinite number of values

  • decimal

  • fraction

Examples include: Weight, height, time, etc.

Continuous Random Variable

A random variable is discrete if it has a finite or countable number of possible outcomes that can be listed.

Discrete Random Variable

Discrete vs Continuous

​Discrete vs Continuous Examples

Probability Distributions

Summary

The distribution of a random variable tells which values a random variable can take on and how often it takes on those values. In doing so, a probability distribution describes a population because when items are sampled from a population, the value observed is the value of a random variable.

-Can be represented as graphs, tables, and formulas

-Can be discrete or continuous

Standard Deviation

The standard deviation on a bell curve is what the x axis is going up and down by. On the graph given, the standard deviation is 5 because the graph is going up and down by 5.

​Empirical Rule / Standard Normal Distribution